Field
The disclosed embodiments relate to batteries for portable electronic devices. More specifically, the disclosed embodiments relate to techniques for using effective C-rates to determine inaccessible capacities of batteries for portable electronic devices.
Related Art
A lithium-ion and/or lithium-polymer battery cell is defined to be fully charged when it is at rest with a voltage of 4.2 V across the terminals. Likewise, the battery cell is defined as fully discharged when it is at rest and the voltage is 3.0 V. The chemical capacity of the cell, called Qmax, is defined as the amount of charge that needs to flow through the terminals to take it from the fully charged state to the fully discharged state. In principle, it would take an infinite amount of time to measure the chemical capacity exactly, since the cell would take an exponentially long time to come to rest. An equivalent definition is that Qmax is the amount of charge that flows through the terminals when the voltage is brought from 4.2 V to 3.0 V, using an infinitely small current.
It has been known for over a century that if a realistic, non-zero current is used to discharge any kind of battery cell, the amount of charge available in going from the full-state voltage to the empty-state voltage is less than the idealized value Qmax. In general, this actually available capacity decreases as the current increases. For lead acid batteries, this capacity loss has been quantified, and is known as Peukert's Law.
For lithium-ion and/or lithium-polymer cells used in portable computers, it is important to be able to estimate this capacity loss, because the computer needs to be able to estimate when the battery will be nearly empty, so that it can save data and shut down safely. The lost capacity, known as the inaccessible capacity, typically amounts to about 3% to 10% of the battery capacity, so for a battery that lasts 2 hours, this makes a difference of about 10 minutes in the run time, which is significant; misjudging the reserve can lead to data loss. Unfortunately, there is no simple quantitative expression for the capacity loss of a lithium-ion cell, and in any case, the current is rarely constant in a modern portable computer, so any such expression would have to take dynamic effects into account.
Approaches to this problem have typically involved taking a simple model of the lithium-ion battery, fitting the model to some measured data to extract parameters, and then solving some equations to estimate the inaccessible capacity for any particular system current. In addition to dealing with the fact that any simple model is wrong, an added complication is that the parameters may need to change as the battery ages, or temperatures change, so some way is needed to continually adapt the parameters to the changing conditions. With this approach, it is in the end very hard to see how accurate the inaccessible capacity estimate actually is, and there is often the danger that continual parameter updates will end up walking the model into some obscure corner of the parameter space, where it gets trapped.
Hence, what is needed is a mechanism for adapting an inaccessible capacity estimate of a battery to changing conditions associated with use of the battery.